I love this Regina Spektor song, “Samson.”
The lyrics are worth looking at because it is an unconventional song. Most popular contemporary songs are structured like this:
Samson doesn’t have a traditional chorus. It does have two repeating lines which begin and end the song and which are also used as a sort of chorus, except with added lines in the middle. For me, the fact that the song doesn’t follow the traditional pattern makes it feel as if I’m listening to someone tell her story in a very intimate, organic way.
Check it out, and try writing your next song with an non-traditional structure.